Otimização aplicada ao risco bancário utilizando um modelo matemático epidemiológico
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2020-02-20
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Universidade Estadual Paulista (Unesp)
Resumo
Este trabalho utiliza um modelo epidemiológico para analisar o comportamento de crises bancárias que possuem origem em um determinado país e são propagadas para outros países atingindo proporções mundiais. O modelo matemático epidemiológico Suscetíveis, Infectados e Recuperados (SIR) empregado permite simular a dinâmica da crise separando os países em três estados: suscetíveis, infectados e recuperados, em cada instante de tempo, além de prever a extensão da crise. Os parâmetros do modelo são obtidos da literatura para cada país envolvido e a crise segue uma dinâmica diferente dependendo do país de origem. Uma breve descrição da importância dos bancos em nível macroeconônico e suas funções básicas são apresentadas. Também são apresentadas algumas definições desta crise, denominada crise sistêmica, bem como os canais de transmissão de como um banco com problemas financeiros, denominado infectado, transmite esta condição para outro. Considerada a possibilidade de uma crise sistêmica, o Banco Central deve intervir nos bancos com problemas. Esta tarefa pode ser modelada como um problema de controle ótimo inserindo uma variável de controle no modelo SIR, que representa a intervenção do Banco Central, e uma função objetivo, em que o custo dessa intervenção deve ser minimizado. O objetivo deste trabalho é investigar um modelo de otimização aplicado ao risco bancário e propor o método heurístico \textit{Variable Neighbourhood Search} (VNS) para resolução do problema de controle ótimo proposto. Vários cenários foram simulados e os resultados computacionais indicam que o modelo de otimização considerado e o método de resolução proposto são boas ferramentas para analisar a propagação de uma crise assim como melhor orientar a forma de ação do Banco Central para o controle da mesma.
This work uses an epidemiological model to analyze the behavior of bank crises that originate in a given country and are propagated to other countries reaching worldwide proportions. The epidemiological mathematical model Susceptible, Infected and Recovered (SIR) used allows to simulate the dynamics of the crisis separating the countries in three states: susceptible, infected and recovered, in each instant of time, in addition to predicting the extent of the crisis. The model parameters are obtained from the literature for each country involved and the crisis follows a different dynamic depending on the country of origin. A brief description of the importance of banks at the macroeconomic level and their basic functions is presented. Some definitions of this crisis, called systemic crisis, are also presented, as well as the transmission channels of how a bank with financial problems, called infected, transmits this condition to another. Considering the possibility of a systemic crisis, the Central Bank must intervene in troubled banks. This task can be xiv modeled as an optimal control problem by inserting a control variable in the SIR model, which represents Central Bank intervention, and an objective function involving the cost of this intervention and must be minimized. The objective of this work is to investigate an optimization model applied to banking risk and propose the Variable Neighborhood Search (VNS) heuristic method to solve the proposed optimal control problem. Several scenarios were simulated and the computational results indicate that the considered optimization model and the proposed resolution method are good tools to analyze the propagation of a crisis as well as to better guide Central Bank’s form of action to control it.
This work uses an epidemiological model to analyze the behavior of bank crises that originate in a given country and are propagated to other countries reaching worldwide proportions. The epidemiological mathematical model Susceptible, Infected and Recovered (SIR) used allows to simulate the dynamics of the crisis separating the countries in three states: susceptible, infected and recovered, in each instant of time, in addition to predicting the extent of the crisis. The model parameters are obtained from the literature for each country involved and the crisis follows a different dynamic depending on the country of origin. A brief description of the importance of banks at the macroeconomic level and their basic functions is presented. Some definitions of this crisis, called systemic crisis, are also presented, as well as the transmission channels of how a bank with financial problems, called infected, transmits this condition to another. Considering the possibility of a systemic crisis, the Central Bank must intervene in troubled banks. This task can be xiv modeled as an optimal control problem by inserting a control variable in the SIR model, which represents Central Bank intervention, and an objective function involving the cost of this intervention and must be minimized. The objective of this work is to investigate an optimization model applied to banking risk and propose the Variable Neighborhood Search (VNS) heuristic method to solve the proposed optimal control problem. Several scenarios were simulated and the computational results indicate that the considered optimization model and the proposed resolution method are good tools to analyze the propagation of a crisis as well as to better guide Central Bank’s form of action to control it.
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Controle ótimo, Crise bancária, Crise sistêmica, Metaheurística, Busca em variância variável, Modelo SIR, Optimal control, Bank crisis, Systemic crisis, Metaheuristic